Examples of topologically unknotted tori, with András Juhász. Preprint.
Simple homotopy types of even dimensional manifolds, with Csaba Nagy and John Nicholson. Preprint.
Pseudo-isotopies of simply connected 4-manifolds, with David Gabai, David T. Gay, Daniel Hartman, and Slava Krushkal. Preprint.
Smoothing 3-manifolds in 5-manifolds, with Michelle Daher. Preprint.
Unknotting nonorientable surfaces, with Anthony Conway and Patrick Orson. Preprint.
Mapping class groups of simply connected 4-manifolds with boundary, with Patrick Orson. Preprint.
4-manifolds with boundary and fundamental group ℤ, with Anthony Conway and Lisa Piccirillo. Preprint.
Stably diffeomorphic manifolds and the realisation of modified surgery obstructions, with Anthony Conway, Diarmuid Crowley, and Joerg Sixt. Preprint.
The Kervaire-Milnor invariant in the stable classification of spin 4-manifolds, with Daniel Kasprowski and Peter Teichner. Preprint.
The 4-dimensional disc embedding theorem and dual spheres, with Arunima Ray and Peter Teichner. Preprint.
Homotopy classification of 4-manifolds with finite abelian 2-generator fundamental groups, with Daniel Kasprowski and Benjamin Ruppik. Preprint.
The foundations of four-manifold theory in the topological category, with Stefan Friedl, Matthias Nagel and Patrick Orson. Accepted for publication in the New York Journal of Mathematics Monograph Series.
Brunnian exotic surface links in the 4-ball, with Kyle Hayden, Alexandra Kjuchukova, Siddhi Krishna, Maggie Miller, and Nathan Sunukjian. Accepted for publication in Michigan Math. Journal.
Algebraic criteria for stable diffeomorphism of spin 4-manifolds, with Daniel Kasprowski and Peter Teichner. Accepted for publication in Memoirs of the American Mathematical Society.
Embedding surfaces in 4-manifolds, with Daniel Kasprowski, Arunima Ray, and Peter Teichner. Accepted for publication in Geometry & Topology.
Gluck twists on concordant or homotopic spheres, with Daniel Kasprowski and Arunima Ray. Accepted for publication in Mathematical Research Letters.
Simple spines of homotopy 2-spheres are unique, with Patrick Orson. Proceedings of the London Mathematical Society, Volume 128 (2024): e12583.
Infinite homotopy stable class for 4-manifolds with boundary, with Anthony Conway and Diarmuid Crowley. Pacific Journal of Mathematics, Volume 325 (2023), No. 2, 209–237.
Simply-connected manifolds with large homotopy stable classes, with Anthony Conway, Diarmuid Crowley, and Joerg Sixt. Journal of the Australian Mathematical Society, Volume 115, Issue 2, 172 - 203, October 2023.
Embedded surfaces with infinite cyclic knot group, with Anthony Conway. Geometry & Topology, Volume 27 (2023) 739 - 821.
Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group, with Allison N. Miller. Journal of the London Mathematical Society, Volume 107, Issue 6, 2025 - 2053, June 2023.
The ℤ-genus of boundary links, with Peter Feller and JungHwan Park. Revista Matemática Complutense, Volume 36, Issue 1 (2023), 1 - 25.
Doubly slice knots and metabelian obstructions, with Patrick Orson. Journal of Topology and Analysis, Volume 14, Number 4 (2023), 847 - 873.
Counterexamples in 4-manifold topology, with Daniel Kasprowski and Arunima Ray. EMS Surveys in Mathematical Sciences, Volume 9, no. 1 (2022), 193 - 249.
A ribbon obstruction and derivatives of knots, with JungHwan Park. Israel Journal of Mathematics, Volume 250, Issue 1 (2022), 265 - 305.
Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials, with Stefan Friedl, Takahiro Kitayama, Lukas Lewark, and Matthias Nagel. Canadian Journal of Mathematics, Volume 74, Issue 4 (2022), 1137 - 1176.
Four-manifolds up to connected sum with complex projective planes, with Daniel Kasprowski and Peter Teichner. American Journal of Mathematics, Volume 144, Number 1, February 2022, 75 - 118.
Characterisation of homotopy ribbon discs, with Anthony Conway. Advances in Mathematics, Volume 391, 19 November 2021, 107960.
Embedding spheres in knot traces, with Peter Feller, Allison N. Miller, Matthias Nagel, Patrick Orson, and Arunima Ray. Compositio Mathematica, Volume 157, Issue 10 (2021), 2242 - 2279.
Two-solvable and two-bipolar knots with large four-genera, with Jae Choon Cha and Allison N. Miller. Mathematical Research Letters, Volume 28, Number 2 (2021), 331-382.
The round handle problem, with Min Hoon Kim and Peter Teichner. Pure and Applied Mathematics Quarterly, Volume 17, Number 1 (2021), 237-247.
A lower bound for the doubly slice genus from signatures, with Patrick Orson. New York Journal of Mathematics, Volume 27 (2021), 379-392.
Triple linking numbers and surface systems, with Christopher W. Davis, Matthias Nagel and Patrick Orson. Indiana University Mathematics Journal, Volume 69, no. 7 (2020), 2505-2547.
Homotopy ribbon concordance and Alexander polynomials, with Stefan Friedl. Archiv der Mathematik, Volume 115 (2020), 717-725.
Whitney towers and abelian invariants of knots, with Jae Choon Cha and Kent E. Orr. Mathematische Zeitschrift, Volume 294 (2020), 519-553.
A family of freely slice good boundary links, with Jae Choon Cha and Min Hoon Kim. Mathematische Annalen, Volume 376, Issue 3 (2020), 1009-1030.
Stabilization distance between surfaces, with Allison N. Miller. L'Enseignement Mathématique, Volume 65 (2019), 397-440.
Smooth and topological almost concordance, with Matthias Nagel, Patrick Orson and Jung Hwan Park. International Mathematics Research Notices, Volume 2019, Issue 23, December 2019, 7324-7355.
Satellites and concordance of knots in 3-manifolds, with Stefan Friedl, Matthias Nagel and Patrick Orson. Transactions of the American Mathematical Society 371 (2019), 2279-2306.
Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance, with Allison N. Miller. Algebraic & Geometric Topology 18 (2018), 3425-3476. Here is a Maple program that implements our algorithm.
Twisted Blanchfield pairings and decompositions of 3-manifolds, with Stefan Friedl, Constance Leidy and Matthias Nagel. Homology, Homotopy and Applications 19, Issue 2 (2017), 275-287.
Stable classification of 4-manifolds with 3-manifold fundamental groups, with Daniel Kasprowski, Markus Land and Peter Teichner. Journal of Topology 10 (2017), 827-881.
Splitting numbers of links, with Jae Choon Cha and Stefan Friedl. Proceedings of the Edinburgh Mathematical Society Volume 60, Issue 3 (2017), 587-614.
Grope metrics on the knot concordance set, with Tim D. Cochran and Shelly Harvey. Journal of Topology 10 (2017), 669-699.
A calculation of Blanchfield pairings of 3-manifolds and knots, with Stefan Friedl. Moscow Mathematical Journal, Volume 17 (2017), Issue 1, 59-77.
The four genus of a link, Levine-Tristram signatures and satellites. Journal of Knot Theory and its Ramifications, special memorial edition in honour of Tim Cochran, Vol. 26, No. 2, (2017).
Concordance invariance of Levine-Tristram signatures of links, with Matthias Nagel.
Documenta Mathematica 22 (2017), 25-43.
Minor revision from the published version.
Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, Volume 67 (2016), Issue 4, 715-742.
Casson towers and slice links, with Jae Choon Cha. Inventiones Mathematicae 205 (2016), Issue 2, 413-457.
Blanchfield forms and Gordian distance, with Maciej Borodzik and Stefan Friedl.
Journal of the Mathematical Society of Japan 68 (2016), no. 3, 1047 - 1080.
Minor revision from the published version.
Embedded Morse theory and relative splitting of cobordisms of manifolds, with Maciej Borodzik. Journal of Geometric Analysis 26 (2016), no. 1, 57-87.
A specious unlinking strategy, with Stefan Friedl and Matthias Nagel. Periodica Mathematica Hungarica 69 (2014), no. 2, 207-210.
Shrinking of toroidal decomposition spaces, with Daniel Kasprowski. Fundamenta Math. 227 (2014), 271-296.
Non-concordant links with homology cobordant zero framed surgery manifolds, with Jae Choon Cha. Pacific Journal of Mathematics 272-1 (2014), 1-33.
Covering link calculus and the bipolar filtration of topologically slice links, with Jae Choon Cha. Geometry & Topology 18 (2014), 1539-1579.
Concordance of links with identical Alexander invariants, with Jae Choon Cha and Stefan Friedl. Bull. London Math. Soc. 46 (2014), No. 3, 629-642.
Links not concordant to the Hopf link; with Stefan Friedl. Math. Proc. Camb. Phil. Soc. 156 (2014), 425-459.
Cobordisms to weakly splittable links, with Stefan Friedl. Proc. Amer. Math. Soc. 142 (2014), 703-712.
Cosmetic crossings and Seifert Matrices; with Cheryl Balm, Stefan Friedl and Effie Kalfagianni. Communications in Analysis and Geometry 20 (2012), 235-253.
An Injectivity Theorem for Casson-Gordon Type Representations relating to Knot and Link Concordance, with Stefan Friedl. Bulletins of the KMS 49 (2012), No. 2, 395-409.
A second order algebraic knot concordance group, a shorter version of my thesis. Algebraic & Geometric Topology 12 (2012), 685-751.
Smoothly slice boundary links whose derivative links have nonvanishing Milnor invariants,
with Hye Jin Jang and Min Hoon Kim. Michigan Math. Journal 63 (2014), No. 2, 423-446.
The proof that our links are smoothly slice
contains what seems to be a serious mistake: the embedding Y x I does not exist as claimed on pages 16 and 17.
My PhD thesis on a second order algebraic knot concordance group.